Finite Group DatabasebetaFinite Group DatabasebetaOrder 4352.
542 conjugacy classes of subgroups; only the 139 normal subgroups are shown.
This group has 542 conjugacy classes of subgroups — too many to draw. Only its 139 normal subgroups are shown.
Dotted edges: containments with no intermediate normal subgroup — omitted non-normal subgroups may lie between.
Splittings G = N ⋊ H with N normal; H ≅ G/N.
| N | H ≅ G/N | type |
|---|---|---|
| 1. C2×D16×D17 | C2 | semidirect |
| 2. C2×D544 | C2 | semidirect |
| 3. C2×#11762644 | C2 | semidirect |
| 4. D17×D32 | C2 | direct (N × H) |
| 5. C2×C32×D17 | C2 | semidirect |
| 6. C2×C17×D32 | C2 | semidirect |
| 8. C2×D272 | C22 | semidirect |
| 11. D16×D17 | C22 | semidirect |
| 13. D544 | C22 | semidirect |
| 14. #11762644 | C22 | semidirect |
| 15. C2×#10587465 | C22 | semidirect |
| 16. C32×D17 | C22 | semidirect |
| 17. C2×C17×D16 | C22 | semidirect |
| 18. C17×D32 | C22 | semidirect |
| 19. C2×C17×C32 | C22 | semidirect |
| 28. C17×D16 | C23 | semidirect |
| 33. D272 | C23 | semidirect |
| 36. C17×C32 | C23 | semidirect |
| 37. #10587465 | C23 | semidirect |
| 79. C2×D32 | D17 | direct (N × H) |
| 87. C2×D17 | D32 | direct (N × H) |
| 97. C2×D16 | C2×D17 | semidirect |
| 101. D32 | C2×D17 | direct (N × H) |
| 104. C2×C32 | C2×D17 | semidirect |
| 106. C2×C17 | C2×D32 | semidirect |
| 109. D17 | C2×D32 | direct (N × H) |
| 121. D16 | C22×D17 | semidirect |
| 127. C32 | C22×D17 | semidirect |
| 128. C17 | C22×D32 | semidirect |
| 179. C2 | D17×D32 | direct (N × H) |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×D16×D17 | 2 |
| C2×D544 | 2 |
| C2×#11762644 | 2 |
| D17×D32 | 2 |
| C2×C32×D17 | 2 |
| C2×C17×D32 | 2 |
| C22×D32 | 17 |